EBD_7137 Ifa and b (60) are vo quanti ofthe sme kind ten the faton & i lle he ratio of a ‘+ Ratio is denoted by the symbol "=" + Fora ratio, the two quantities must be in the same unit, ‘+ Ratio is expressed in its simplest form cannot be further simplified. ‘hs oF ato is and dant whe ala anes! ands cl onsen When the two terms of a ratio have no common factor other than 1, we say that ratio is in simplest form. + To reduce a ratio in simplest form, first write ratio as faction and then divide the numerator and denominator by their C.F, ‘There are 350 boys and 250 girls in a school. Find the ratio of boys to girls in the simplest form or lowest term, Boys = 350, Girls = 250 Ratio of ee HF of 250 and 350 is 50 tio of boys to gils = So = Se of 250 and 350 is $0) or 7:8 NOTE : (i) Ratio always exists between two quantities of same kind and unit Ratio, being a fraction have no unit A ratio does not change if its numerator and denominator are multiplied or divided by a non-zero number. (iv)_The order of the terms are very important ie. 7:8 ¢ 8:7 The present age of mother is 48 years and that of her daughter is 16 years. Find the ratio of : (The present age of mother to present age of daughter. ii) The age of mother and daughter after 6 years. (iii) The age of mother to the age of daughter when daughter was 6 years old.ati and rporton fil SOLUTION : (The present age of the mother to the present age of daughter. Present age of mother = 48 years Present age of daughter = 16 years 48 48e16 3 Required ratio= 48 16= T= Ee = pa 3i (ii) The age of mother and daughter after 6 years. After 6 years age of mother = 48 + 6 ~ 54 years. ‘After 6 years age of daughter = 16 + 6 = 22 years 4 ca Required rao = 54: 22= 5 = DO = = 27s th (iii) The age of mother to the age of the daughter when the daughter was 6 years old. Daughter was 6 years old 10 years ago Mother's age 10 years ago = 48 ~ 10 = 38 years 383822 _ 19 nog mig= 8 = 822. ayy. ILLUSTRATION : 3 (4 hrs to 400 minutes (i 2 dozens to 4 scores (i) 4 brs = 4 = 60 = 240 minutes sto = 240: a0p = 2 — 240290 3 (ii) 4 scores = 4 » 20 = 80 2 4 _ M8 3 Equivalent Ratios ‘A ratio obtained by multiplying or dividing the numerator and denominator by thesame number is alled an equivalent ratio, ILLUSTRATION : 4 Find two equivalent ratios of 5 : 9. SOLUTION : To find equivalent ratios ofS : 9, multiply both the terms by 2 and then 3. 5_5x2_ 10 5 Sx3_15 5-52 and 5 = 23-1 -15:97 5 9x2 1g 2818845 9.3727 ‘Thus, 10: 18 and 15 : 27 are two equivalent ratios of 5 : 9. ILLUSTRATION : 5 Fill in the blank box: uO & a 3EBD_7137 653] temas SOLUTION : tet 4 = then, 21r= 14 3 > x= 483 Say > 3 Then 2 arr 2_6 6x3 4 Asin, lat = then, 2y = 6x 3=y= 855 <9 Hence, SF = Dividing some quantity in the given ratio 4 pq . P When we have to divide a quantity ‘xin the ratio p : g, then two parts are —P—xx and —2—xx quantity Ped parts are 7 ILLUSTRATION : 6 Divide 7 1250 between Mayank and Ishi SOLUTION : ‘Total money = € 1250 and given ratio 7 rf sya sare =(Zore12s0}= e129 22) = € 50 = [jerense]-e(1a9-3) ILLUSTRATION : 7 Divide @ 1200 among A, B and C in the ratio 2:3: 5. SOLUTION : Total money = € 1200 Sum of ratio terms = (2 +3 + 5)= 10 2 : «(10-2 «{1n0s3) GO Eas ‘Suppose we want to compare two given ratios, Then, we express each one of them as. fraction inthe simplest form, Now, compare these fractions by making their denominators equal ILLUSTRATION : 8 Compare the ratios 9 : 16 and 3 : SOLUTION : Here, 360, Csshare@ (2005) 9 3 osu and 3:45 7 16 9 3 Now; let us compare 7¢ and 7. The LCM of 16 and 4 is 16. Making the denominator of each fraction equal {0 16, we have:Iai and Proportion fl 9 9x1 9 3 3x4 12 16 ~ 6x1 16 9 4 > 4x4 16 29 3 9 Te? 16 Pa? 1g Hence, 34> 9: 16 Toni) Proportion is defined as an equality of two ratios, Four (non-zero) quantities ofthe same kind a,b, cand dare said to bein proportion ifthe ratio ofa to b is equal tothe ratio of eto d Clearly, ie, if $=£ bd We can write as a:b::e:d Here, a,b,c, dare in proportion and are respectively known as first, second, third and fourth term of the given proportion. Here, the Ist and 4th terms are called the extreme terms or extremes. The 2nd and 3rd terms are called the ‘middle terms or means. We can also say, in proportion, Product of extremes = Product of means Ifa, b, ¢, d are in proportion then, bd i.e, Product of extremes = Product of means ILLUSTRATION : 9 Are the numbers 40, 30, 60 and 45 in proportion? SOLUTION : Given terms are 40, 30, 60 and 45 Product of extremes = 40 * 45 = 1800 Product of means = 30 60 = 1800 Product of extremes = Product of means Thus 40, 30, 60 and 45 are in proportion. Alternate method: oraxd=bxe 60 + Ratio of 60 t0 45 = Te = 5 Both the ratios are equal. Therefore the numbers are in proportion, ILLUSTRATION : 10 Radha purchased 14 toffees for €35 and Geeta purchased 12 toffees for € 30, Who bought more expensive toffees? Ratio of 40 a» - 2 cio of 01030 = SOLUTION : Ratio of the number of toes purchased by Radha to the number of toflees purchased by Geeta: 4: 12=7:6 Ratio of their costs = 35 : 30= 7: 6 Both ratios, 14 > 12 and 35 : 30 are equal Thus, both purchased the toffees for the same price ILLUSTRATION : 11 Find the value of x in the proportion S : 10EBD_7137 63} $$ $$ $$$ etna SOLUTION : Product of extremes = Product of means 5x30 So, $x 30= 10x x or x= => 15 Thus, ILLUSTRATION : 12 For every 20 oranges that Raj buys, 4 turns out tobe rotten. Att will he have if he buys 100 oranges? SOLUTION : ‘The ratio of rotten oranges to the oranges bought is 4 : 20. Let, Raj has x rotten oranges if he buys 100 oranges Therefore, the ratio of rotten oranges tothe oranges rrate, how many rotten oranges bought is x : 100, Then, 4:20=x: 100 Now Product of extremes = Product of means 4100 34 * 100 = 20% x > “SO =x 20=x or x=20 Thus Raj has 20 rotten oranges if he buys 100 oranges Mae) ‘The method in which first we find the value of one unit and then the value of required number of units by ‘multiplying the value of one unit with the number of required units. ILLUSTRATION : 13 A car travels 240 ki in 4 hours. How for does it trav SOLUTION : We have, Distance travelled in 4 hours= 240 km -. Distance travelled in I hou Hence, the distance travelled in 7 hours = (60 7) = 420 km ILLUSTRATION : 14 The weight of 72 books is 9 kg. (@ What is the weight of 40 such books? Gi) How many books will weight 45 kg? SOLUTION : i) Weight of 72 books = 9 kg = Weight of 1 book = 9 Weight of 40 books = = * 40 = 5 kg (ii). 9 kg is the weight of 72 books n > 1 kg is the weight of “> books n 4.5 kg is the weight of “>> 4.5 = 36 books.ati and rporton fil CONCEPT MAP Ratio Equivalent Ratio Ifa and b (b+ 0) are two quantities of the same kind, then the fraction b. It is denoted by ‘a : b! where ‘a! is called antecedent and'b is called consequent’ iscalled ratio of aand A ratio obtained by multiplying dividingthe numerator and denominator by the same number is called an equivalent ratio. For example ETS CEI Hai uae) Unitary Method Proportion “The method in which first we find the value of one unit and then the value of required number of units bby multiplying the value of one unit with the number of required units. + Four non-zero quantities ofthe same kind a,b, candd are said to bein proportion, if the ratio ofa to b is equal tothe ratio of ¢ odie, or ad=be Weean write as arbsre:dnaa} 1. Express each of the following ratios in the simplest form. @ 3:49 (i) 3kg 15g: 450g (ii) $ dozen : 6 scores 35_ 3557 (i) Wehave 35:49= = =o Sol. 5 [Dividing both numerator and denominator by 7, the H.C.F. of 35 and 49] Gi) We have 3 kg 15 g: 450 g= 3015 g:450¢ 3015 _ 3015+45 45045045 [Dividing both numerator and denominator by 45, the H.C.F. of 3015 and 450] 67 To 7670 (iii) We have S dozen : 6 scores=5 « 12:6% 20 60 oo SF [Dividing bth 120 120. numerator and denominator by 60, the H.C, of 60 and 120) = 60: 120= 2 2 2. Write the ratio of the following : @ 1mto50cm (i) 500 gto2 kg. Sol. (i) Here, two terms are | m and SO em respectively So, we have to express both the terms in the same unit of measurement. Now, we convert metre into centimetre, So, Im = 100m Ratio of Im to 50m -—_ Dine} SOLVED E)(AMPLES—— Sol. Sol. Sol. Sol. EBD_7137 Mathematics (ii) Here, we convert 2 kilograms into grams. So, 2 kg = 2000 g 1 The length and the bréadth of a reetangular park are 75 m and 60 m respectively. What the rato ofthe lengthtothe breadth of thepark? = 75:60 [+ HCF of 75 and 60 is 15} Hence, the required ratio is 5:4, ‘Two numbers are in the ratio 7 :3 and their sum is 600. Find the numbers. Let the first number be 7x and the second number be 3x ‘Then, theit sum = 7x + 3x lor ‘The first number = 7x ‘The second number = 3x = 3 (60) Compare the ratios 2: S and 4:7. 180 2 5 and4 ‘The L.CM. of Sand7= 5 7=38 22x74 axs_ 20 5 sep 35 ™ 7 7x5 35 We have 2 Now, since 20>14, -. 20> 14 35°35 3 4:7 2:5 Find three equivalent ratios of 3: 4. 4,2 Pas Weave sean 322223334 4 4x20 4x3 4x4Iai and Proportion fi Sol. Sol. Sol. ged 6 9 2 7 4781216 = 3:4=6:8=9:12= 12:16 Hence, each one of 6 : 8,9: 12 and 12: 16 is equivalent to 3:4, Check if 20,25, 12 and 15 are in proportion, 120,25, 12 and 1S are in proportion, then 20:25 should be equal to 12:15. 204 BoA ea:5 Alternate method Product of extremes = 20 * 1 Product of means =25 « 12 =300 Since the product ofextremes = Product of means 20, 25, 12 and 15 are in proportion, ‘The Ist, 3rd and 4th terms ofa proportion are 18, 27 and 36 respectively. Find the 2nd term. Let the 2nd term ofthe proportion be x. Then, 18x: :27:36. oduct of extremes. 00 Now, product of means, 18x36 8x 36=4= 5S =24. Hence, the 2nd term ofthe given proportion is 24, On a map, a length of 4 em is used to represent a distance of 250 km, Ifthe actual distance between the two places is 6250 km, find the corresponding distance on the map. Ifthe distance between two big cities on the map is 20 em, find the actual distance between these twocities. A distance of 250 km is represented on the map by4em. A distance of | kim is represented on the map, 4 by 555 om, xx27 A distance of 6250 km is represented on the Sol. Sol. ts ie 6250) em= 100. Phy 590250) ‘Thereguzed distance on themap is 1m, Again edsance oft cmon te maprewesent 20k ‘distance of | on onthe map represents 250 Jon, 4 ‘A distance of 20cm on the map represents (72-20 }hm= 1250 ra) ‘The required actual distance between the two cities is 1250 km, A rectangular sheet has 3 m length and 200 cm breadth. Find the ratio of: (a) Its width to its length (b) Its width to its perimeter. Length (2) = 3m =3 = 100=300 em Breadth (b) = 200 em Perimeter = 2 (/ +b) = 2 (300+ 200) 2» $00 = 1000 em, (a) Ratio of its width to its length 200 2 ~ 300 7 3 (b)- Ratio of its width to its perimeter 200 1 1000” 5 An office opens at 10 a.m. and closes at 6 p.m. vith a lunch interval of 30 minutes. What the ratio of lunch interval to the total period of the office? Total time from 10 am. to6 pam hrs x 60 minutes = 480 minutes Ratio of the lunch interval to total period 30minutes 480 minutes le(]} enats EXERCISE GUO DIRECTIONS: Complete the following statements ‘with an appropriate word / term to be filled in the lant space(s T 2 2 4 Doa-s 5 830: 8215 6 Says 13 boys ws R370 & 90em:15m 9.1836: 81:3: 63 then 10. comparison by aalleda radio M1. Ina proportion, the fist and the fourth terms are called Dare DIRECTIONS: Read the following statements and rite your answer as true or fase. T 2 3. 4 geen T)_To tind the ratio of two quantities, we must express them in the same units An equivalent ratio of 2: 3 is 18 : 27, The simplest form of ratio 625 : 225 is 25 : 10. distance travelled bya car in 3 hrs is 120 km then distance travelled by car in S hrs is 240 km, ‘Ashish made 42 runs in 6 overs and Anup made 63,runsin 7 overs, Ashish made more runs per Akl purchased 10 pens for €150 and Manish buys 7 pens for & 84. Akul bought cheaper pens. 30, 40, 45, 60 are in proportion. 6:8 and9 + 12 are equivalent ratios of 3 : 4 DEK DIRECTIONS : Each question contains statements given in two columns which have to be matched. ‘Statements (A, B, C, D) in column-I have to be ‘matched with statements (p,q. 8) in columnetI 1 Column-1 (A) The length and width of a tape are 2 m and 28 em, ratio of length and breadth is (B) Ratioof 60 hrst0 —— (q) 61 (600 min is (C) Simplest form ofthe (6) $027 ratio 125: 25 is (D) Inthe word ENGLISH (8) 5:1 the ratio of number of consonants to number of vowels (Oren cas DIRECTIONS : Give answer in one word or one sentence, Column-t () 5:2 1. Inthe given figure, find the ratio of (i) No. of shaded parts to unshaded parts (i) No. ofunshaded parts to the total number of pauts PRE Prac ls 2. Express the folowing ratios into simplest form (i) 240 om to a metre Gi) 40 min to 2 hes EBD_7137Iai and Proportion fi 10. ML 2. (iii) 50 paise to 4 rupees Gv) 4 days to 2 weeks (¥) $00 g to 2ke (vi) 108 to 360 ‘The present ages of Ravi and Tanya are22 years and 16 years, respectively, Find the ratio of Their present ages (ii) Ravi’s age to the difference of their ages. (ii) Ravi age after 4 years to Tanya's age 3 years ago (iv) Ravis age to that of Tanya's when she was 5 yeras old Radha has 3 white marbles, 4red marbles and. 10 stones find the ratio of marbles to stones. Fill in the blanks with = or = @ 12 Kgto 15 Kg [] & 28 to 835 i) 201030 [84 0k6 (ii) 60 m to 72 m [] 48 m to 60 m liv) € 4500 to € 400 [] & 2500 to € 3000 ) 2LwsLesmen What i the ratio ofthe number of sides ofa quae tothe numberof edges ofa cube? Neolam’s annual income is © 288000, Her annual savings amount to% 36000, whats the ratio of her savings toher expenditure? Teravel 12m in 3 hours by sand 315 km in S hours by train Find ratio of speed ofthe bus and speed of the train Ashok i 25 years old and Anant is 10 yeas 6 months old. Find the rato ofthe age of Anant tothat of Ashok The length and breadth ofa stel tape are 10m and 2.4m, respectively. The atioof the length tothe breadth is Find the ratio ofthe east prime numb othe least composite numb. Express the fllowing ratios in the simplest form: (i) 55.508 (i) So paise: €10 Gi) 2 e300 e:3 kg Gv) 2h4Omin: 1 day (v) Sf: 10cm (vi) 2h: 15s (si 3 dozen #4 Scores (oii) & 5.50: 8 15.75 (Gx) 200 m2 km Ena orc DIRECTIONS : Give answer in 2-3 sentences. 1. Show that the numbers 16, 28, 4, 7 form a proportion. 2, 1f25, 35, xarein proportion, find the value of x 3. Theratioof father's age and his son’s age is 5 2. I the father's age is 50 years, what is his son's age? 4. Find the cost of 1S kg. of sugarif’§ kg. of sugar costs 7 88 5. A bus covers 250 km in $ hours. How much. distances will it cover in 12 hours? 6. Ratio of number ofboys to number of girls in a tutorial is 2: 3. Ifthere are 180 girls, then find the number of boys. 7. Twonumbers arein the ratio 5: 4and their sum. is 162, Find the numbers. 8. Incach of the following paits of ratios, find the ratio which is greater: (7: Mands:12 (i) 19:31 and3:5 (iil) €5.40: © 3.60 and 3kg :2 ky 500 g (iv) 1h 30min : 4830 min and 600m: 1 km 700m 9. ‘The ratio of zine and copper in a brass piece is 13:7, How much zine will be there in 100 kg. of such a piece ? 10. Divide € 40 in the ratio of 3: 2 EEE DIRECTIONS : Give answer in four to five sentences 1. The weight of 72 books is 9 kg. () Whatis the weight of 40 such books? ii) How many books will weight 4.5 ke? 2. The ratio of the number of girls to that of boys in a school is 7 : 12. Ifthe number of boys in the schoo! is 1380, find (i) the number of girls inthe schoa! and (ii the total numberof students inthe school.(] temas 3. Awoman worker earns ® 18000 in 15 months. (How much does she earn in 7 months? i) In how many months will she earn % 300007 4. ‘The weight of 72 books is 9 ke, (9) Whatis the weight of 80 such books? ii) How many such books weight 6 ke? EXERCISE Ronn 1. Cost of a toflee is $0 paise and cost of a chocolateis € 10, Find the rai of the eos of a tle 1o the cst ofa chocolate 2. Fill inthe allowing Banks: i G0 0 8” 6 [] 30 Are these equivalent ratios? 3. Find the ratio ofthe following (i) 81 to 108 fi) 981063 Gi) 33 km to 121 km Civ) 30 minutes to45 minutes 4. Find the ratio of the following (i) 30 minutes to 1.5 hours fi 40emt0 15m Gi) $5 paise v0 I (iv) 500 ml to 2 litres 5 Mother wants to divide €36 between her daughters Shreya and Bhoomika in theratio ot their ages. age of Shreyas 15 yeas and age of Bhoomika is 12 years, ind how much money Shreya and Bhoomika will gt 6 Present age of father is 42 years and that of his son is 14 years, Find theratio of (i) Present age of father to the present age of (i) Age ofthe father tothe age of son, when son was 12 years old Gi) Age of father ater 10 years tothe age of son after 10 years. (iv) Ageoffther othe age ofson when father was 30 yeas ol 7. Determine if the flowing are in proportion, (i) 15,45, 40,120 (ii) 33, 121, 9,96 Gi) 24,28, 36,48 (iv) 32,48, 70,210 8 Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion. (25cm: 1 mand &40: € 160 ii) 39 litres 65 litres and 6 bottles : 10 botles (iil) 2 kg: 80 kg and 25 g:625 g Gv) 200 ml: 2.5 litreand 4; © 50 9. Ifithas rained 276 mm in the ast 3 days, how ‘many em of rain will fll in one full week (7 days)? Assume that the rain continues to fall at the same rate, 10, Cost of 5 ky of wheat is & 30.50. (What will be the cost of 8 kg of wheat? Gi) What quantity of wheat can be purchased in G61? 1 car travels 90 km in 2; hours. 11, Acar travels 90 km in 25h (i) How much time is required to cover 30 km with the same speed? (ii) Find the distance covered in 2 hours with the same speed Reshma prepared 18 kg of burfi by mixing khoya with sugar in the ratio of 7:2. How much, khoya did she use? 2. Anooffice opens at 9 am. and closes at 5:30 p.m. with a lunch break of 30 minutes, What isthe ratio oflunch break tothe total period inthe office? 3. Theshadow of a 3 mong stick is 4 m long, At the same time of the day, if the shadow of a flagstafTis 24 m long, how tall is the flagstaff? 4. Arecipe calls for I cup of milk for every a4 cups of flour to make a cake that would feed EBD_7137ati and Proportion fil 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 persons? 5. Ina floral design made from tiles each of dimensions 40 em by 60 em (see fig.), find the ratios of, the perimeter of shaded portion to the perimeter of the whole design, (ii) the area of the shaded portion to the area of the unshaded portion, i 6. ‘The earth rotates 360° about its axis in about 24 hours. By how much degree will it rotate in 2 hours? 7. ‘The quarterly school fee in Kendriya Vidyalaya for Class VI is © 540, What will be the fee for seven months? 8% In-an election, the votes cast for two of the candidates were in the ratio $ : 7, If the successfl candidate received 20734 votes, how many votes did his opponent receive? 9, A metal pipe 3 metre long was found to weigh 7.6 kg. What would be the weight of the same kind of 7.8 m long pipe? 10, A recipe for raspberry jelly cals for S cups of | sapere 2! pfs: Fd amount of sugar needed for 6 cups of the juice? Goer 1. A tea merchant blends two varieties of tea costing her & 234 and ® 130 perky in the ratio oftheir costs Ifthe weight of the mixture is 84 kg, then find the weight of each variety of tea, 2 Length and breadth of the floor of a room are Smand 3m, respectively. Forty tiles, each with, Ls . area 7¢1?areused to ‘cover the floor partially. Find the ratio of the tiled and the non tiled portion of the floor. 3. A carpenter had a board which measured 3m * 2m, She cut out a rectangular piece of 250em x 90em, What is the ratio ofthe area of cut out piece and the remaining piece? 4, Sunil and Anil together have 650 in the ratio 8: S respectively. Ifthey both spend 50 each, then what will be the ratio of the amounts left with them ? EXERCISE EI DIRECTIONS : This section contains multiple choice questions. Each question has 4 choices (a). (®). (0) and (A) out of which ONLY ONE is correct. ‘The ratio of savings to expenses is 2: 7. Ifthe expenses are € 3,500, then what was the total (@) © 7,000 (b) & 5,000 (©) © 4,500 (@ © 5,500 2. Ina box, theratioofred marbles to blue marbles is 7 : 4. Which of the following could be the total number of marbles in the box?” (@) 18 (b) 19 © 21 @ 2 3. Onashelf; books with green cover and that with brown cover are in theatio2 :3. fthereare 18 books with green cover, then the number of bbooks with brown cover is @ 12 (b) 24 © 27 (a) 36(] temas 4 10. nL. 2. The ratio of wo numbers isa: b. [fone of them fsx, then other is ab 6 Os o x ax a & © a @ > In a cricket coaching camp, 1200 children are trained out of which 900 are selected for various ‘matches. Ratio of non-selected children to the ‘otal number of children is (a) 300: 120 (b) 4:1 () 14 (a) 120: 300 m: 32:24: 16 value of mis (@) 16 ) 8 4 @ 2 ‘There are *b’ boys and *g” girls in a class. The ratio of the number of boys tothe total number of students im the class is ® & bee OF ery 1500 sheets are required to make 100 notebooks. How many sheets will be required tomake 12 note books? (@) 180 (b) 200 (©) 120 (@) 100 To make a cup of tex ratio of water to milk is 3 1. So to make 4 cups of tea the ratio of water tomilkis (@) 4:31 (b) 12:1 (e) 12:4 (@) 4212 Inthe word MATHEMATICS the ratio of number of consonants to the number of vowels is (a) 407 () 74 (e) 5:6 (a) 6:5 Inaquiz programme the ratio of correct answers to incorrect answers is 5 : 2. If 16 incorrect answers are given then the number of correct answers given is (@) 80 (b) 40 © 20 (@) 30 Ajay and Vijay start @ business investing % 18000 and 24000 respectively. At the end of the year Ajay receives € 9000 as his share in profit, What was the total profit made? (@) © 21000 (© © 18000 (b) © 24000 @ © 15750 (Chirk kore DIRECTIONS : Phis section contains multiple choice questions. Each question has 4 choices (a). (0). (c) and (d) out of which ONE or MORE may be correct. 1 Ratio of 60 hrs, 0 600 min. is (@) 3600 : 600 (b) 1:6 © 6:1 @ Sil ‘The ratio of @ 3 and 60 paise is (@ 1:20 (b) S21 1:2 () 20:4 Ratio of 250 ml to 2 Lis (@ 25: 200 (b) 8:1 © 1:8 (@) 2:1 Inan office the working hours are 10.30 AM to 530 PM and in between 30 minutes are spent ‘on lunch. Find the ratio of office hours to the time spent for lunch. (@ 420:30 (by Ltd @ Met (@) 30:7 Equivalent ratio to 3:4 are @ 4:3 (b) 9212 © 2:3 @ 15:20 Which of the following is an equivalent ratioof 4:9 (a) 818, (© 17:13 (b) 28:63 (@) 16:36 Gener DIRECTIONS : Each of these questions contains ‘an Assertion followed by Reason, Read them carefully ‘and answer the question on the basis of following ‘options. You have to select the one that besi describes the owo statements (a) (b) fboth Assertion and Reason are correct and Reason is the correct explanation of Asserti Irboth Assertion and Reason are correct, but Reason is not the correct explanation of Asser EBD_7137Iai and Proportion fil (©) If Assertion is correct but Reason is incorrect. (@) Assertion is incorrect but Reason is correct. 1. Assertion: 3: 5::9: 15 are equivalent ratios, Reason : Both ratios are equal, when simplified, 2. Assertion: If 3, 10, 15, 50 are in proportion, then 3 and 50 are middle terms and 10. and 15 are extreme terms, Reason : If a,b,c, dare in proportion then a andd are extreme terms nd band c are middle terms, 3. Assertion : An equality of two ratios is called ‘proportion Reason : Four quantities a, b,c, d are said (0 be in proportion ite ELE DIRECTIONS : Study the given passage(s) and answer the following questions. PASSAGE-1 Prateek runs an ice eream parlour. He earns €3500 per month, He is able to save 1400 but spends the rest, Find the ratio of 1. Prateck’s income tohis expenditure (a) 5:2 (b) 5:3 ©) 35 @ 25 2, Prateek’sincome tohis saving. (@) 5:2 (b) 2:5 © 5:4 (@) 4:5 3. Prateck’s expenditure to his saving. (a) 2:3 (b) 5:3 © 3:5 (a) 3:2 PASSAGE. Read the information given below carefully and answer the questions that follows. “The ratio of the price of a pencil to the price of an eraser is 5:1” 4. Which of the following object is more expensive? (a) Braser (b) Pencil (©) Both (a) None of these 5. Ifthe priceof the pencil is 210, can the priceof the eraser be % 20? (a) No () yes (©) can'tsay (@)_Datais insufficient 6. Ifthe price of the eraser is € 1, then what will be the price ofthe pencil ? @ % (bo) %4 (©) &5 @ %0 Cees DIRECTIONS : Answer the following questions. The answer to each ofthe question isa single digit integer ranging from 0 109. 1. Weight of 45 bags ofrice is 900 kg. How many. bags of rice have a weight 140 kg? 2. If :6::x: 18 then find the value of. 3. Ifthe simplest form of the ratio 13 : 65 is 1:. What is the value of y? 4. Ina box containing 30 bulbs, 5 are found defective. The ratio of defective to good bulbs ised. Find the value of ¢ + 5. The cost of 8 chocolates is ® 56. What will be the cost of | chocolates Multiple Matching Question : DIRECTIONS : Following question has four statements (A, B, C and D) given in Column-L and sixstatements (p,q. 18. t, in Columnll. Any given statement in Column-I can have correct matching with one or more statement(s) given in Column 1. Match the following. Column-L Column. (A) Ratio of 6 daysto p35 2 weeks is (B) Ratioof9kmto gq. 1:4 18mis (©) Ratioof 18 mmto $00: 1 Bemis (D) 3months tol years. 1EBD_7137 Deas GUE Lo WS ST 5 1kg328¢ 6 1235 cows 7029 & 3:5 % x= 28 10, division 11. extremes Eis 1, True 2. True 3. False 4, False 5. False 6 False 7 True 8. True 9. False 10. True DE L(A): B)>@(C) >; D) >) Az length=2m = 200m breadth = 28 em Cs 18:28 Dz Number of consonant= 5 Ratio of no, of consonants tothe no. of vowels = 5:2 LODE one rs Low 1:2 2 fi) 12:5 Gi) 1:8 w lsd 3) 8 (iil) 221 (iy) es 4 7:10 & fi) = Gi) + w= 6 13 Road 8 We know that speod 126 kmh Speed of bus = “> : Ratio of speeds 9. Anant’s age 42:63 =2:3 10 years 6 months =10 £ L195 = 10 years 5 = 10.5 years Ratio of Anant’s age and Ashok’s age _ 10s _ 21 © 105525" 195 ~ 50 10. 1250:3 11, Least prime : Least composite number =2:4 of 1:2 12. () Ust01 i) 1:20 Gi) 5:6 Gv) 1:9) $0021 (vi) 48021 (i) 9:20 (vil22:63 ix) 1:10 Ee ered 1. The given trems are 16, 28, 4,7. 6x 7= 112. 8x 4= 112. +. Product of extremes = Product of means, Hence, 16,28, 4, 7 are in proportion. 2. 25,35,.rare in proportion "25,35, 35, xare in proportion 5 2S1381235sx = Se y=35%35 [product of extremes = product of means}Iai and Proportion fl 35x35 2 Hence, x= 49, 3. Let the son's age be. years. Then $ :2=50:x Sy=2* 50 250 3 Hence, the son's age is 20 years. 4. Cost of Ske. of sugar = T88 Cost of 1 kg. of sugar = Cost of 1S ke. ofsugar= SS 5 $ = € 165 5. Distance covered in hours = 250 km. Dis ed in 1 he = 74, tance covered in I hour = 72" kim Distance covered in 12 hour 250 2 sc12 = 600km 5 600 kx 6 Boys togirls=2:3 Boys = 120 7. Let the required numbers be Sx and 4x. Then, Sy +4x= 162 = 9v= 162, So, the numbers are (5 * 18) and (4 * 18), i.e, 90 and 72. & fj) 8:12 (iii) 75.40: 83.60 (iv) 600m: 1 km 700 m 9. Sum ofratios= 13+7=20 Gi) 19:31 B rantity of zine ~ > +100 ~ 65 Ke. Quantity x = Sum of terms of ratio=3 +2 Ist part of & 40 peat = 224 5. 2nd pat of €40= 7 *AO" = € 16, Long Answer Questions : 1.) Weight of 72 books =9 ke 9 = Weight oft book = 2 kg we 2 x 40- eight of 40 books = 75% 40= 5 kg (ii) 9 kgs the weight of 72 books n =I kgis the weight of “> books R 4 Skgisthe weightof “5 %4.5=36books 2. Itis given that ratio of girls to boys = 7:12. (i) Let the number of girls in the schoo! be x. then, 1380 x: 1380 S 12ex= 7% 1380 [Product of means = Product of extremes] 71380 2 Number of girls in the schoo! = 805, (ii) Total number of students in the school = (805 + 1380) = 2185. > x 3.) Wehave, Income for 15 months = € 18000 100) Income for I month = @ [Fz Hence, income for 7 months 18000 : ) . ( 1s ) = %(1200% 7)= % 8400, Thus, she earns ® 8400 in 7 months.EBD_7137 (]} ena (ii) In this case, the number of months is ‘unknown quantity and the income is the known quantity. So, we proceed as fallows: Number of months required to earn € 1800015 Number of months required to earn -( Is ) 1 i000, Hence, number of months required to earn = ¥ 30000 ( 5.30000 | = 25 i000") Thus, she willearn € 30000 n 25 months Wehave, Weight of 72 books = 9 kg 9 Weight of | book = +> kg Hence, weight of 80 books ° (200) ke= 10 kg ‘Thus, the weight of 80 books is 10 ke. (ii) Here, weight isthe known quantity andthe ‘number of books is the unknown quantity So, we proceed as follows. ‘The number of books in 9 kg of weight =72 ‘The number of books in 1 ky weight “Hence, the number of books in 6 kg weight = 8 6=48, ‘Thus, the number of books in 6 kg weight is 48, iia: ew 1. Cost of chocolate = % 10 = 1000 paise Le. &1= 100 paise] Cost of toffee Cost of chocolate Ratio. 3 _ 50 1000 ~ 20 1:20 1 []s18*D-10«18 toss a Hep 15430 15 81227 108+27 33km 12Ikm 121-11 \Ominutes 30-152 Sminutes 45-15 3 2 '3 (iil) Ratio= 3:1 no (iv) Rati 30minutes _30minutes 1Shour “ 90 minutes [tshour=F5¢ominis=90 mints | 0 30302301 == 3 4dcm_ 40cm 15m 150emIai and Proportion fi] [stm=Moem :15m= 40 40510 4 150” 150210 ~ 15 (ii) Ratio of $5 paise to @ Ls €1=100 paise] 100 10025 [HCE of $5 and 100 is 5] Pease GR F502 ie 500 Sime ie 1000m soon _ soo 2000 nt 2000 [> HCF of 500 and 2000 is 500] 00500 1 4.4 2000+500 4” Isyem _ 1583. 5 5 Ratotteirages= S28 = 1853. Sum of the ratios = 5 +4=9 5 Shreya's share=& 5 « 36= € 20 4 Bhoomiks’s share = € 5 x36= € 16 Ageof father 6G) 2 Ratio Age oFson years ~ Ta years 14514 (ii) Obviously when son's age was 12 years (ic. 2 years ago), then father’s age was (42 years 2 years) = 40 years Ratio of father’s age to son's age 40 years 4024 10 IDyears 124 ~ 3 (Gil) After 10 years Age of father = 42 years + 10 years = $2 years ‘Age of son = 14 years + 10 years = 24 years Ratio of father’s age to son's age _ Sdyears 52-4 13 ~ Dayears 24=4 ~ 6 (iv) 9. 42-30-12 12 years age, age of father was = 30 years and. 12 years age, age of son was = 14 years 12 years = 2 years Ratio of father's age the son's age =10:3 13:6 1s 2years 242 1ST (Ratio of 15 and 45 = 15:45 1S_1Ss15_1 “45 45e15 3 [+ HCP of 1S and 45 is 15] Ratio of 40 and 120 = 40: 120 40 40240 1 ~i20 120=40~ 3 [HCE of 40 and 120 is 40) 15:45:40: 120 iy 33,121, 9, 96 Here, ratio of 33 and 121 = 33 33s 3 “ia ie i Ratio of 9 and 96=9 : 96 ~ 22283 3 ~ 96 "9623-32359? Since, 3: 11 43:32 33, 121, 9 and 96 are notin proportion, 2121 (iil) 24, 28, 36, 48; Ratio of 24 and 28 = 24 : 28 24 6 p67 Ratio of 36 and 48 = 36:48EBD_7137 65] temas wv) “i i) 3636412 3 48 48212" 4 ie6:743:4 or 24:28 7 36:48, 24,28, 36 and 48 are not in proportion. 32,48, 70, 210 Ratio of 32 and 48 = 32: 48, 23246 24, 48 48516 3 Ratio of 70 and 210 = 70 _ 70270 1 210 2102703 Since 2:341:3 i.e. 32:48%70:210 32, 48, 70, 210 are not in proportion, 25225 1 25em_2Sem Im 100em 100=25. 4 240 and €40: & 160= 3565" 6p 40240 1 4 160=40 4 Since, both the ratios are equal, ‘They form a proportion, Now, middle terms are Im and & 40 and extreme terms are 25 em and & 160. 39litres We have, 39 lites 65 littes= SStitres 393981334 6 oi 3° and 6 bottles : 10 bottles 6 6523 10 10+ Since, both the ratios are equal 39 itres : 65 ites: :6bottles: 10 battles lismidale terms are 65 litres and 6 bottles Weave, 2 kg : 80 kg - 2-22 11.49 ~ 0° 8022 40 and 25 g: 625 10. 25 _ 25225 _ ~ 625” 62! Since 1:40 1:25 ‘The given ratios do not form a proportion (iv) 200 ml: 2.5 litres 200ml __ 200 mi © 2S litres 2.51000m1 [Litre = 1000 mt} _ 200, 200100 2, 4, ~ 2500 2500=100 25 and &4: &50 a4 Since the two ratios are equal, i.e, 200 ml : 2.5 litres = €4: €50 ‘They form a proportion Its middle terms are 2.5 litres and & 4. Its extreme terms are 200 ml and ® 50. Measure of rainfall in 3 days =276 mm ‘Measure of rainfall in 1 day = 276 gam =92 mm 3 So, measure of rainfall in 7 days = (02 7)_mm_ Seas mi (0. Cost ofS ky of wheat = @ 30.50 3050 Cost of kg of wheat = & 2252 og 0,1 7 S100 10 a So, cost of8 kg of wheat= & (SB = 2 88 _ 2 as.80 =e Gi) Quantity of wheat that can be purchased a for & Ty = 1 ke Quantity of wheat that can be purchased fore = 22 for €1= kgati and Proportion fi So, quantity of wheat that can be purchased bao x61 kg=10kg. ‘Thus, (i) Cost of 8 kg of wheat is & 48.80 (ii) 10 kg of wheat can be purchased in @ 61 mn (i) 50 minutes 90 km is covered in 150 minutes Therefore, 1 km can be covered in 130 130 nutes canbecoveredin 222 ‘Therefore, 30km can becovered in “32 30 minutes i.e, $0 minutes ‘Thus, 30 km can be covered in $0 minutes. (ii) Distance, covered in 2+ hours 3 (is. 5 hours)=90 km ‘Therefore, distance covered in I hours 6 km 0 = 5 km=90 « 2km= ‘Therefore, distance covered in 2 hours 6x 2= 72 km, ‘Thus, in 2 hours, distance covered is 72km. Brn 1, Total weight of burfi = 18 kg. Sum of ratios 2 Quantity of khoya = | 5*18 |ke= 14 ke 2. Time duration between 9a.m, and 5.30pm, hr+5 hr 30min, = 8 hr 30min, x 60 +30 10 min, ‘The ratio of lunch break to total period in the office = 30: $10 3001 sio 77 3 4, Let the height of lagstaff be x meter. a bekor Mate east Mins oraeo see perns = Lup. Milk needed for eake to serve 8 persons Flour need fr cake seve 8 persons _ Sat 10 = Ea cape ‘Total quantity offlour and milk Dimensions of each tile is 40 em by 60 em, 0.em d pe ||socm D © () ». AB=4% 60.em=240em x 40 em = 200 em Perimeter of whole design 2 (240+ 200) = 880 em EF=2 60 em=120em FG=3 40.em=120em Perimeter of shaded portion =2(120+ 120) = 480 ‘The ratio of the perimeter of shaded portion to the perimeter of the whole design = 480 : 880 6: (ii) Since each tilecovers samearea and number of tiles covering shaded portion = 6. Number of tiles covering unshaded portion =14